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Grade: 12
        If a+2b=6 then find Maxima of ab and a²b. Pleaseget me solution I am eager to know this
2 years ago

Answers : (6)

akhil
11 Points
							
this should be done by differentiating seperately i mean partial differention the other way is that to sub no other way than this the best way is partial differentiation
2 years ago
Yogesh Kumar
43 Points
							
a+2b=6
For maximum value both of them should be equal.
so, a=b for max. value
3a=6, a=2=b
So max value of ab=3 x 3=9
     and that of a2b=32 x 3=27
2 years ago
Yogesh Kumar
43 Points
							
sorry there is mistake in above answer. So here is the correct explanation for this
We can apply AM>or=GM here
so for finding max value of ab
(a+2b)/2>or=(2ab)1/2
32>or=2ab
ab
and for finding max value of a2b
we have write a+2b=a/2+a/2+2b
now (a/2+a/2+2b)/3>or=(a2b/2)1/3
23>or=a2b/2
so a2b4 so max value of a2b is 24
2 years ago
Rohit
47 Points
							
 
sorry there is mistake in above answer. So here is the correct explanation for this
We can apply AM>or=GM here
so for finding max value of ab
(a+2b)/2>or=(2ab)1/2
32>or=2ab
ab
and for finding max value of a2b
we have write a+2b=a/2+a/2+2b
now (a/2+a/2+2b)/3>or=(a2b/2)1/3
23>or=a2b/2
so a2b4 so max value of a2b is 24sorry there is mistake in above answer. So here is the correct explanation for this
2 years ago
Rohit
47 Points
							
 
sorry there is mistake in above answer. So here is the correct explanation for this
We can apply AM>or=GM here
so for finding max value of ab
(a+2b)/2>or=(2ab)1/2
32>or=2ab
ab
and for finding max value of a2b
we have write a+2b=a/2+a/2+2b
now (a/2+a/2+2b)/3>or=(a2b/2)1/3
23>or=a2b/2
so a2b4 so max value of a2b is 24
2 years ago
Hashit Katiyar
12 Points
							
a +2b = 6 
a = 6-2b
Now, 
        ab= 6b-2b2
For maxima and minima,
         (d/db){6b-2b2} = 0
                6-4b = 0
then,        b = 3/2
                d2/db2{6b-2b2} = -4     …....for all vlaues of d
             Hence, ab is maximum for b = 3/2 
             ab = 9/2 for b = 3/2
             Similarly, we can get a2b = 16.   
      
            
2 years ago
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